| abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr10, adr0 = adr4, adr1 = adr8, adr2 = adr7, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0), remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx0 ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro, jmaxino1 ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino1, p_os < pmaxino, ri.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), inv(gstore1 \ jro), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), node-cons(nd6.key, nd6), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), node-cons(nd3.key, nd3), refsize-cons(gstore, range ri), refsize-cons(gstore0, range fi1), refsize-cons(gstore1, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino1, ri.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, dom gstore ⊆ dom gstore1, ⌊err1⌋ , ¬ dups(nx0), ¬ dups(nx), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟨choose adr1, adr2, adr3, adr4 with new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ') in {adr7 := adr1, adr8 := adr2, adr0 := adr3, adr := adr4; fs := fs[adr7, nd6][adr8, nd5][adr0, nd4][adr, nd3], log := (((log + adr7) + adr8) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC; jvalid := ?⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr2 = adr7 ∧ adr1 = adr8 ∧ adr4 = adr0 ∧ adr10 = adr ∧ err1 = err), ⟨fail#(; ; err); adr3 := ?, adr2 := ?, adr0 := ?, adr := ?; jvalid := ?⟩ ((jvalid → jvalid1) ∧ adr7 = adr3 ∧ adr8 = adr2 ∧ adr4 = adr0 ∧ adr10 = adr ∧ err1 = err) |
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr10, adr0 = adr11, adr5 = adr8, adr6 = adr7, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0), remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino1, p_os < pmaxino, jro1 < jmaxino1, inv(gstore1 \ jro), inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), node-cons(nd3.key, nd3), node-cons(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd6.key, nd6), refsize-cons(gstore1, range ri), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino1, dom gstore ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ri.lebs ⊆ dom gstore1, ⌊err1⌋ , jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ (∀ adr1, adr2, adr3, adr4. ¬(new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 '))) ∧ ⟨err := ENOSPC; jvalid := ?⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr6 = adr7 ∧ adr5 = adr8 ∧ adr11 = adr0 ∧ adr10 = adr ∧ err1 = err), ∃ adr1, adr2, adr3, adr4. (new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ')) ∧ ⟨adr7 := adr1, adr8 := adr2, adr0 := adr3, adr := adr4; fs := fs[adr7, nd6][adr8, nd5][adr0, nd4][adr, nd3], log := (((log + adr7) + adr8) + adr0) + adr, err := ESUCCESS; jvalid := ?⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr6 = adr7 ∧ adr5 = adr8 ∧ adr11 = adr0 ∧ adr10 = adr ∧ err1 = err), ⟨fail#(; ; err); adr9 := ?, adr6 := ?, adr0 := ?, adr := ?; jvalid := ?⟩ ((jvalid → jvalid1) ∧ adr7 = adr9 ∧ adr8 = adr6 ∧ adr11 = adr0 ∧ adr10 = adr ∧ err1 = err), jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx)